A team of engineers is designing a new water reservoir. They model the depth of the water, $h(t)$ (in meters), in the reservoir as a function of time $t$ (in days) since the start of the rainy season. The rate of change of the water depth is given by $h’(t) = 0.2t - 0.01t^2$, for \$0 \le t \le 30$. At the start of the rainy season, the reservoir is empty, i.e., $h(0) = 0$.
a. Determine the exact depth of the water in the reservoir after 30 days, expressing your answer as a definite integral and evaluating it.
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Create Free Account Log inThis is a free VCE Units 3 & 4 Mathematical Methods practice question worth 3 marks, testing your understanding of Definite Integral as Limit. It falls under Calculus in Unit 3: Mathematical Methods Unit 3. Submit your answer above to receive instant AI-powered marking and personalised feedback.
Extend introductory study of functions, algebra, calculus. Focus on functions, relations, graphs, algebra, and applications of derivatives.
Covers limits, continuity, differentiability, differentiation, and anti-differentiation.
informal consideration of the definite integral as a limiting value of a sum involving quantities such as area under a curve and approximation of definite integrals using the trapezium rule
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